2x+20+x+40+1/2x+50=180

Solution for 2x+20+x+40+1/2x+50=180 equation:

2x+20+x+40+1/2x+50=180

We move all terms to the left:

2x+20+x+40+1/2x+50-(180)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

3x+1/2x-70=0

We multiply all the terms by the denominator


3x*2x-70*2x+1=0

Wy multiply elements

6x^2-140x+1=0

a = 6; b = -140; c = +1;
Δ = b2-4ac
Δ = -1402-4·6·1
Δ = 19576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{19576}=\sqrt{4*4894}=\sqrt{4}*\sqrt{4894}=2\sqrt{4894}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-140)-2\sqrt{4894}}{2*6}=\frac{140-2\sqrt{4894}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-140)+2\sqrt{4894}}{2*6}=\frac{140+2\sqrt{4894}}{12}
$